Topology of broken Lefschetz fibrations and near-symplectic 4-manifolds

Details Topology of broken Lefschetz fibrations and near-symplectic 4-manifolds Topology of broken Lefschetz fibrations and near-symplectic 4-manifolds

2007-12-31

arxiv.org/abs/0801.0192v2

Mathematics

Geometric Topology

26 pages, 12 figures. Shorter title and fewer typos

Scientific paper

The topology of broken Lefschetz fibrations is studied by means of handle decompositions. We consider a slight generalization of round handles, and describe the handle diagrams for all that appear in dimension four. We establish simplified handlebody and monodromy representations for a certain subclass of broken Lefschetz fibrations/pencils, while showing that all near-symplectic closed 4-manifolds can be supported by these a la Auroux, Donaldson, Katzarkov. Various constructions of broken Lefschetz fibrations and a generalization of the symplectic fiber sum operation to the near-symplectic setting are given. Extending the study of Lefschetz fibrations, we detect certain constraints on the symplectic fiber sum operation to result in a 4-manifold with nontrivial Seiberg-Witten invariant, as well as the self-intersection numbers that sections of broken Lefschetz fibrations can acquire.

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